Question

Find the angle between the x-axis and the line joining the points (3, -1) and (4, -2).

Answer 1

Given:

The line joins the points A(3, −1) and B(4, −2).

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Step 1: Find the slope of the line

Slope (m) =

m = (y₂ − y₁) / (x₂ − x₁)

m = (−2 − (−1)) / (4 − 3)

m = −1 / 1 = −1

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Step 2: Find the angle with the x-axis

If θ is the angle which the line makes with the positive x-axis, then:

m = tan θ

tan θ = −1

θ = −45°

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Step 3: Angle between the line and the x-axis

The angle between a line and the x-axis is taken as the acute angle.

So,

Angle = 45°

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Final Answer:

The angle between the x-axis and the given line is 45°.